y=(1+2cot"x) 3 dy_ 8(1-2cot"x) dy 8(1+2cotx)° %3D dx 1-x dx 1+x? Op tion 3 Op tion 1 dy -8(1–2cot" x)' 1-x dx None of these Op tion 4 dy_ -8(1+2cot"x)' dx 1+x? Op tion 2

Q: 21. 3* 3=*-x+'(12x² – 4) dx

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Q: Assume x and y are functions of t. Evaluate dx = 9, x = 3, y = 0. for 4xe = 12 - In 729 + 6ln x,…

A: Given query is to find indicated derivative.

Q: Find the ff value in the matrices. PART I IF P= A+B find the value of the following # 1 P1 # 4 P21 #…

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Q: Find the general solution of the differential equation dx = xin (xy)

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Q: Find the general solution of the given ODE * dy 3z+2y dr 3= -23x+2y +c 2=-23x+2y +C O Option 1…

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Q: Evaluate the following Integrals: sin(4t) – 3 sin(2t)² dt 5 Vsech(4x) tan (4x) dx 1. 6. 7. sinh 3y…

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Q: Match each graph type with its corresponding function.

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Q: L x² cos 2x³ dx? After substitution is performed, which of the following is equivalent to

A: Given that the integrals  To find the evaluate and choose the correct answer

Q: Graph the function. Use the graph to find the indicated limit, if it exists. x20 lim f(x), fx) = -…

A: solution:-f(x)=x3 ,         x≥0-6x  ,    x<0left hand limitlimx→0-f(x)=limx→0--6x=0right hand…

Q: 8. The rationalizing substitutionw + 4 = u² transforms - dw into w+4 A. fu² - 4°du B. 2fu² - 4}du C.…

A: Given: I=∫w2w+4dw  ...1   As we know that; The Power law: ddxxn=nxn-1 And ∫a·fxdx=a·∫fxdx , where a…

Q: 3. Which of the following integrals requires integration by parts? A. S csc°0 de B. S cot*0 csc*0 do…

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Q: Find the length of the curve z(t) = e“ cos(t), y(t) = e“ sin(t) for 0<t<7. %3D Give an exact answer,…

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Q: Find r'(t), r(t,), and r'(t,) for the given value of to r(t) = (e', e²9), to = 0 r'(t) = r(t,) =…

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Q: A jet is flying through a wind that is blowing with a speed of 50 mi/h in the direction N 30° E (see…

A: --------------------------------------- Wind velocity: velocity: 50mphDirection: 30° with…

Q: 12 Let y24xー4x+3 le) Find the eauetion.of the tangent Iine to the graph of the fuuction att x-2; O…

A: We have to find tangent line

Q: Please

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Q: 1. Find the most general antiderivative of the function 12 f(x) = ( 2r + sin(4- r) + 7e

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Q: f (x)= arcsin (x³)+ aretan (4x)

A: derivative

Q: (2x2 + x -3) * (x + 1) a = [21-3]; b = [1 1]; find conv (a, b)

A: Given :2x2+x-3*x+1

Q: g. -3+i

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Q: Give the value(s) of x at whichf has either a local minimum or a local maximum. Give the interval(s)…

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Q: sech2(In x)

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Q: P2: |(e* sin x + x In x) dx

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Q: Find the limit, If it exists. x- 1 lim X---

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Q: d Calculate ri(t) · r2(t)] and d ri(t) x r2(t)] first by differentiating dt' dt the product directly…

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Q: If 0 = Ø and R= 4/2, then F2 = %3D 4V2 F, F, V8 08 O 2 04

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Q: f(x)= sin (x² +2x)

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Q: IV. Suppose z is a function of r and y, and tan Vy² + x² 2e&y¸ Solve for az az and dy

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Use the integral test to determine the convergence or divergence of the series. 00 cos 1/k 21) E k2…

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Q: 23. Find two numbers whose sum is 10 and the sum of their squares is a minimum.

A: Let the two numbers be  x and yx+y=10⇒y=10-xx2+y2=SS=x2+10-x2   =x2+x2-20x+100   =2x2-20x+100

Q: The table above gives values of f, f'. g and g' for selected vahues (A) -14 (В) -13 (C) -2 (D) 7 (E)…

A: We will use integration by parts and will take values from table to solve this.

Q: 1. A soccer ball is kicked with a speed of 75 mph at an angle of 30° from the horizontal. Write the…

A: Given query is to find the velocity components.

Q: dv 4.)Prove that f -Incosv + Insinv + C sinvcosv

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Q: V. Determine all the relative minimum and maximum values, and saddle points of the function h…

A: Solution: Given data, h(x,y)=x3-3x+3xy2

Q: Determine whether F(x, y) = 2x²yi+ 8xy j is a conservative vector field. If so, find a potential…

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Q: Suppose we are given the data in the table about the functions f and g and с. their derivatives.…

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Q: ind the average value of the function over the glven Interval and all values of x In the Interval…

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Q: A firm produces two types of calculators each week, x of type A and y of type B. The weekly revenue…

A: Let's find.

Q: 1) Use the Integral Test to determine whether the series 1 is convergent or divergent. (Зп — 1)? c)…

A: The given series ∑n=1∞1(3n-1)2

Q: Q3/ Find the limits 1. lim 2. lim Vx+2-1 X-1 х+1

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Q: 3) Compute the cross product: x

A: Let vectors are given as       a = 4i-j+2k    &amp;   b = -5i -3j+10k

Q: Use the properties of the derivative to find the following. r(t) = ti + 5tj + t?k, u(t) = 5ti + t?j…

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Q: 1. Find the most general antiderivative of the function f(x)D + sin(4- r) +7e

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Q: Evaluate the line integral. The simple curve is C is y = x² starting at (0, 0) and ending at (1, 1).…

A: We can solve as follows

Q: Jasmine builds tool sheds. She uses 10 sheets of drywall and 15 studs for a small shed and 15 sheets…

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Q: P1: 2 cos-1 x dx 1xo

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Q: y = 4 (2,4) A y = 2x x = 2 B y =x (0,0) Region A is bounded by the lines y= 2x, y= 4 and the y-axis.…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: Determine the vector field of F. F(x, y) = yi – xj

A: Given:     F(x,y) = yi - xj.          ---------(i) We have to determine the vector field of equation…

Q: Find the equation of the tangent line at the given point on the curve. 2y - Vx = 4. (16,2) y =U

A: We need to find equation of tangent line.

Q: The polar equation of the curve is expressed as r = 2sine + 2cose. area bounded by the curve.

A: To find the area.